{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Markov switching dynamic regression models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook provides an example of the use of Markov switching models in statsmodels to estimate dynamic regression models with changes in regime. It follows the examples in the Stata Markov switching documentation, which can be found at http://www.stata.com/manuals14/tsmswitch.pdf."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# NBER recessions\n",
    "from pandas_datareader.data import DataReader\n",
    "from datetime import datetime\n",
    "usrec = DataReader('USREC', 'fred', start=datetime(1947, 1, 1), end=datetime(2013, 4, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Federal funds rate with switching intercept\n",
    "\n",
    "The first example models the federal funds rate as noise around a constant intercept, but where the intercept changes during different regimes. The model is simply:\n",
    "\n",
    "$$r_t = \\mu_{S_t} + \\varepsilon_t \\qquad \\varepsilon_t \\sim N(0, \\sigma^2)$$\n",
    "\n",
    "where $S_t \\in \\{0, 1\\}$, and the regime transitions according to\n",
    "\n",
    "$$ P(S_t = s_t | S_{t-1} = s_{t-1}) =\n",
    "\\begin{bmatrix}\n",
    "p_{00} & p_{10} \\\\\n",
    "1 - p_{00} & 1 - p_{10}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "We will estimate the parameters of this model by maximum likelihood: $p_{00}, p_{10}, \\mu_0, \\mu_1, \\sigma^2$.\n",
    "\n",
    "The data used in this example can be found at https://www.stata-press.com/data/r14/usmacro."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get the federal funds rate data\n",
    "from statsmodels.tsa.regime_switching.tests.test_markov_regression import fedfunds\n",
    "dta_fedfunds = pd.Series(fedfunds, index=pd.date_range('1954-07-01', '2010-10-01', freq='QS'))\n",
    "\n",
    "# Plot the data\n",
    "dta_fedfunds.plot(title='Federal funds rate', figsize=(12,3))\n",
    "\n",
    "# Fit the model\n",
    "# (a switching mean is the default of the MarkovRegession model)\n",
    "mod_fedfunds = sm.tsa.MarkovRegression(dta_fedfunds, k_regimes=2)\n",
    "res_fedfunds = mod_fedfunds.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>y</td>        <th>  No. Observations:  </th>    <td>226</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovRegression</td> <th>  Log Likelihood     </th> <td>-508.636</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Tue, 24 Dec 2019</td> <th>  AIC                </th> <td>1027.272</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>14:58:36</td>     <th>  BIC                </th> <td>1044.375</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>             <td>07-01-1954</td>    <th>  HQIC               </th> <td>1034.174</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                   <td>- 10-01-2010</td>   <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>approx</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    3.7088</td> <td>    0.177</td> <td>   20.988</td> <td> 0.000</td> <td>    3.362</td> <td>    4.055</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    9.5568</td> <td>    0.300</td> <td>   31.857</td> <td> 0.000</td> <td>    8.969</td> <td>   10.145</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Non-switching parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    4.4418</td> <td>    0.425</td> <td>   10.447</td> <td> 0.000</td> <td>    3.608</td> <td>    5.275</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0]</th> <td>    0.9821</td> <td>    0.010</td> <td>   94.443</td> <td> 0.000</td> <td>    0.962</td> <td>    1.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0]</th> <td>    0.0504</td> <td>    0.027</td> <td>    1.876</td> <td> 0.061</td> <td>   -0.002</td> <td>    0.103</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using numerical (complex-step) differentiation."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                        Markov Switching Model Results                        \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                  226\n",
       "Model:               MarkovRegression   Log Likelihood                -508.636\n",
       "Date:                Tue, 24 Dec 2019   AIC                           1027.272\n",
       "Time:                        14:58:36   BIC                           1044.375\n",
       "Sample:                    07-01-1954   HQIC                          1034.174\n",
       "                         - 10-01-2010                                         \n",
       "Covariance Type:               approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          3.7088      0.177     20.988      0.000       3.362       4.055\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          9.5568      0.300     31.857      0.000       8.969      10.145\n",
       "                           Non-switching parameters                           \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sigma2         4.4418      0.425     10.447      0.000       3.608       5.275\n",
       "                         Regime transition parameters                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "p[0->0]        0.9821      0.010     94.443      0.000       0.962       1.002\n",
       "p[1->0]        0.0504      0.027      1.876      0.061      -0.002       0.103\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_fedfunds.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the summary output, the mean federal funds rate in the first regime (the \"low regime\") is estimated to be $3.7$ whereas in the \"high regime\" it is $9.6$. Below we plot the smoothed probabilities of being in the high regime. The model suggests that the 1980's was a time-period in which a high federal funds rate existed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res_fedfunds.smoothed_marginal_probabilities[1].plot(\n",
    "    title='Probability of being in the high regime', figsize=(12,3));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the estimated transition matrix we can calculate the expected duration of a low regime versus a high regime."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[55.85400626 19.85506546]\n"
     ]
    }
   ],
   "source": [
    "print(res_fedfunds.expected_durations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A low regime is expected to persist for about fourteen years, whereas the high regime is expected to persist for only about five years."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Federal funds rate with switching intercept and lagged dependent variable\n",
    "\n",
    "The second example augments the previous model to include the lagged value of the federal funds rate.\n",
    "\n",
    "$$r_t = \\mu_{S_t} + r_{t-1} \\beta_{S_t} + \\varepsilon_t \\qquad \\varepsilon_t \\sim N(0, \\sigma^2)$$\n",
    "\n",
    "where $S_t \\in \\{0, 1\\}$, and the regime transitions according to\n",
    "\n",
    "$$ P(S_t = s_t | S_{t-1} = s_{t-1}) =\n",
    "\\begin{bmatrix}\n",
    "p_{00} & p_{10} \\\\\n",
    "1 - p_{00} & 1 - p_{10}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "We will estimate the parameters of this model by maximum likelihood: $p_{00}, p_{10}, \\mu_0, \\mu_1, \\beta_0, \\beta_1, \\sigma^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Fit the model\n",
    "mod_fedfunds2 = sm.tsa.MarkovRegression(\n",
    "    dta_fedfunds.iloc[1:], k_regimes=2, exog=dta_fedfunds.iloc[:-1])\n",
    "res_fedfunds2 = mod_fedfunds2.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>y</td>        <th>  No. Observations:  </th>    <td>225</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovRegression</td> <th>  Log Likelihood     </th> <td>-264.711</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Tue, 24 Dec 2019</td> <th>  AIC                </th>  <td>543.421</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>14:58:49</td>     <th>  BIC                </th>  <td>567.334</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>             <td>10-01-1954</td>    <th>  HQIC               </th>  <td>553.073</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                   <td>- 10-01-2010</td>   <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>approx</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.7245</td> <td>    0.289</td> <td>    2.510</td> <td> 0.012</td> <td>    0.159</td> <td>    1.290</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.7631</td> <td>    0.034</td> <td>   22.629</td> <td> 0.000</td> <td>    0.697</td> <td>    0.829</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   -0.0989</td> <td>    0.118</td> <td>   -0.835</td> <td> 0.404</td> <td>   -0.331</td> <td>    0.133</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    1.0612</td> <td>    0.019</td> <td>   57.351</td> <td> 0.000</td> <td>    1.025</td> <td>    1.097</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Non-switching parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.4783</td> <td>    0.050</td> <td>    9.642</td> <td> 0.000</td> <td>    0.381</td> <td>    0.576</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0]</th> <td>    0.6378</td> <td>    0.120</td> <td>    5.304</td> <td> 0.000</td> <td>    0.402</td> <td>    0.874</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0]</th> <td>    0.1306</td> <td>    0.050</td> <td>    2.634</td> <td> 0.008</td> <td>    0.033</td> <td>    0.228</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using numerical (complex-step) differentiation."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                        Markov Switching Model Results                        \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                  225\n",
       "Model:               MarkovRegression   Log Likelihood                -264.711\n",
       "Date:                Tue, 24 Dec 2019   AIC                            543.421\n",
       "Time:                        14:58:49   BIC                            567.334\n",
       "Sample:                    10-01-1954   HQIC                           553.073\n",
       "                         - 10-01-2010                                         \n",
       "Covariance Type:               approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.7245      0.289      2.510      0.012       0.159       1.290\n",
       "x1             0.7631      0.034     22.629      0.000       0.697       0.829\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.0989      0.118     -0.835      0.404      -0.331       0.133\n",
       "x1             1.0612      0.019     57.351      0.000       1.025       1.097\n",
       "                           Non-switching parameters                           \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sigma2         0.4783      0.050      9.642      0.000       0.381       0.576\n",
       "                         Regime transition parameters                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "p[0->0]        0.6378      0.120      5.304      0.000       0.402       0.874\n",
       "p[1->0]        0.1306      0.050      2.634      0.008       0.033       0.228\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_fedfunds2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are several things to notice from the summary output:\n",
    "\n",
    "1. The information criteria have decreased substantially, indicating that this model has a better fit than the previous model.\n",
    "2. The interpretation of the regimes, in terms of the intercept, have switched. Now the first regime has the higher intercept and the second regime has a lower intercept.\n",
    "\n",
    "Examining the smoothed probabilities of the high regime state, we now see quite a bit more variability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res_fedfunds2.smoothed_marginal_probabilities[0].plot(\n",
    "    title='Probability of being in the high regime', figsize=(12,3));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, the expected durations of each regime have decreased quite a bit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.76105188 7.65529154]\n"
     ]
    }
   ],
   "source": [
    "print(res_fedfunds2.expected_durations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Taylor rule with 2 or 3 regimes\n",
    "\n",
    "We now include two additional exogenous variables - a measure of the output gap and a measure of inflation - to estimate a switching Taylor-type rule with both 2 and 3 regimes to see which fits the data better.\n",
    "\n",
    "Because the models can be often difficult to estimate, for the 3-regime model we employ a search over starting parameters to improve results, specifying 20 random search repetitions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Get the additional data\n",
    "from statsmodels.tsa.regime_switching.tests.test_markov_regression import ogap, inf\n",
    "dta_ogap = pd.Series(ogap, index=pd.date_range('1954-07-01', '2010-10-01', freq='QS'))\n",
    "dta_inf = pd.Series(inf, index=pd.date_range('1954-07-01', '2010-10-01', freq='QS'))\n",
    "\n",
    "exog = pd.concat((dta_fedfunds.shift(), dta_ogap, dta_inf), axis=1).iloc[4:]\n",
    "\n",
    "# Fit the 2-regime model\n",
    "mod_fedfunds3 = sm.tsa.MarkovRegression(\n",
    "    dta_fedfunds.iloc[4:], k_regimes=2, exog=exog)\n",
    "res_fedfunds3 = mod_fedfunds3.fit()\n",
    "\n",
    "# Fit the 3-regime model\n",
    "np.random.seed(12345)\n",
    "mod_fedfunds4 = sm.tsa.MarkovRegression(\n",
    "    dta_fedfunds.iloc[4:], k_regimes=3, exog=exog)\n",
    "res_fedfunds4 = mod_fedfunds4.fit(search_reps=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>y</td>        <th>  No. Observations:  </th>    <td>222</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovRegression</td> <th>  Log Likelihood     </th> <td>-229.256</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Tue, 24 Dec 2019</td> <th>  AIC                </th>  <td>480.512</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>15:02:11</td>     <th>  BIC                </th>  <td>517.942</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>             <td>07-01-1955</td>    <th>  HQIC               </th>  <td>495.624</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                   <td>- 10-01-2010</td>   <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>approx</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.6555</td> <td>    0.137</td> <td>    4.771</td> <td> 0.000</td> <td>    0.386</td> <td>    0.925</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.8314</td> <td>    0.033</td> <td>   24.951</td> <td> 0.000</td> <td>    0.766</td> <td>    0.897</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.1355</td> <td>    0.029</td> <td>    4.609</td> <td> 0.000</td> <td>    0.078</td> <td>    0.193</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>   -0.0274</td> <td>    0.041</td> <td>   -0.671</td> <td> 0.502</td> <td>   -0.107</td> <td>    0.053</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   -0.0945</td> <td>    0.128</td> <td>   -0.739</td> <td> 0.460</td> <td>   -0.345</td> <td>    0.156</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.9293</td> <td>    0.027</td> <td>   34.309</td> <td> 0.000</td> <td>    0.876</td> <td>    0.982</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0343</td> <td>    0.024</td> <td>    1.429</td> <td> 0.153</td> <td>   -0.013</td> <td>    0.081</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.2125</td> <td>    0.030</td> <td>    7.147</td> <td> 0.000</td> <td>    0.154</td> <td>    0.271</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Non-switching parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.3323</td> <td>    0.035</td> <td>    9.526</td> <td> 0.000</td> <td>    0.264</td> <td>    0.401</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0]</th> <td>    0.7279</td> <td>    0.093</td> <td>    7.828</td> <td> 0.000</td> <td>    0.546</td> <td>    0.910</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0]</th> <td>    0.2115</td> <td>    0.064</td> <td>    3.298</td> <td> 0.001</td> <td>    0.086</td> <td>    0.337</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using numerical (complex-step) differentiation."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                        Markov Switching Model Results                        \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                  222\n",
       "Model:               MarkovRegression   Log Likelihood                -229.256\n",
       "Date:                Tue, 24 Dec 2019   AIC                            480.512\n",
       "Time:                        15:02:11   BIC                            517.942\n",
       "Sample:                    07-01-1955   HQIC                           495.624\n",
       "                         - 10-01-2010                                         \n",
       "Covariance Type:               approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.6555      0.137      4.771      0.000       0.386       0.925\n",
       "x1             0.8314      0.033     24.951      0.000       0.766       0.897\n",
       "x2             0.1355      0.029      4.609      0.000       0.078       0.193\n",
       "x3            -0.0274      0.041     -0.671      0.502      -0.107       0.053\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.0945      0.128     -0.739      0.460      -0.345       0.156\n",
       "x1             0.9293      0.027     34.309      0.000       0.876       0.982\n",
       "x2             0.0343      0.024      1.429      0.153      -0.013       0.081\n",
       "x3             0.2125      0.030      7.147      0.000       0.154       0.271\n",
       "                           Non-switching parameters                           \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sigma2         0.3323      0.035      9.526      0.000       0.264       0.401\n",
       "                         Regime transition parameters                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "p[0->0]        0.7279      0.093      7.828      0.000       0.546       0.910\n",
       "p[1->0]        0.2115      0.064      3.298      0.001       0.086       0.337\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_fedfunds3.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>y</td>        <th>  No. Observations:  </th>    <td>222</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovRegression</td> <th>  Log Likelihood     </th> <td>-180.806</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Tue, 24 Dec 2019</td> <th>  AIC                </th>  <td>399.611</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>15:02:11</td>     <th>  BIC                </th>  <td>464.262</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>             <td>07-01-1955</td>    <th>  HQIC               </th>  <td>425.713</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                   <td>- 10-01-2010</td>   <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>approx</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   -1.0250</td> <td>    0.292</td> <td>   -3.514</td> <td> 0.000</td> <td>   -1.597</td> <td>   -0.453</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.3277</td> <td>    0.086</td> <td>    3.809</td> <td> 0.000</td> <td>    0.159</td> <td>    0.496</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.2036</td> <td>    0.050</td> <td>    4.086</td> <td> 0.000</td> <td>    0.106</td> <td>    0.301</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    1.1381</td> <td>    0.081</td> <td>   13.972</td> <td> 0.000</td> <td>    0.978</td> <td>    1.298</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   -0.0259</td> <td>    0.087</td> <td>   -0.298</td> <td> 0.766</td> <td>   -0.196</td> <td>    0.145</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.9737</td> <td>    0.019</td> <td>   50.206</td> <td> 0.000</td> <td>    0.936</td> <td>    1.012</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.0341</td> <td>    0.017</td> <td>    1.973</td> <td> 0.049</td> <td>    0.000</td> <td>    0.068</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.1215</td> <td>    0.022</td> <td>    5.605</td> <td> 0.000</td> <td>    0.079</td> <td>    0.164</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 2 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.7346</td> <td>    0.136</td> <td>    5.419</td> <td> 0.000</td> <td>    0.469</td> <td>    1.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.8436</td> <td>    0.024</td> <td>   34.798</td> <td> 0.000</td> <td>    0.796</td> <td>    0.891</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.1633</td> <td>    0.032</td> <td>    5.067</td> <td> 0.000</td> <td>    0.100</td> <td>    0.226</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>   -0.0499</td> <td>    0.027</td> <td>   -1.829</td> <td> 0.067</td> <td>   -0.103</td> <td>    0.004</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Non-switching parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.1660</td> <td>    0.018</td> <td>    9.138</td> <td> 0.000</td> <td>    0.130</td> <td>    0.202</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0]</th> <td>    0.7214</td> <td>    0.117</td> <td>    6.147</td> <td> 0.000</td> <td>    0.491</td> <td>    0.951</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0]</th> <td> 4.001e-08</td> <td>    0.035</td> <td> 1.13e-06</td> <td> 1.000</td> <td>   -0.069</td> <td>    0.069</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[2->0]</th> <td>    0.0783</td> <td>    0.057</td> <td>    1.372</td> <td> 0.170</td> <td>   -0.034</td> <td>    0.190</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->1]</th> <td>    0.1044</td> <td>    0.095</td> <td>    1.103</td> <td> 0.270</td> <td>   -0.081</td> <td>    0.290</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->1]</th> <td>    0.8259</td> <td>    0.054</td> <td>   15.201</td> <td> 0.000</td> <td>    0.719</td> <td>    0.932</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[2->1]</th> <td>    0.2288</td> <td>    0.073</td> <td>    3.126</td> <td> 0.002</td> <td>    0.085</td> <td>    0.372</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using numerical (complex-step) differentiation."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                        Markov Switching Model Results                        \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                  222\n",
       "Model:               MarkovRegression   Log Likelihood                -180.806\n",
       "Date:                Tue, 24 Dec 2019   AIC                            399.611\n",
       "Time:                        15:02:11   BIC                            464.262\n",
       "Sample:                    07-01-1955   HQIC                           425.713\n",
       "                         - 10-01-2010                                         \n",
       "Covariance Type:               approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -1.0250      0.292     -3.514      0.000      -1.597      -0.453\n",
       "x1             0.3277      0.086      3.809      0.000       0.159       0.496\n",
       "x2             0.2036      0.050      4.086      0.000       0.106       0.301\n",
       "x3             1.1381      0.081     13.972      0.000       0.978       1.298\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.0259      0.087     -0.298      0.766      -0.196       0.145\n",
       "x1             0.9737      0.019     50.206      0.000       0.936       1.012\n",
       "x2             0.0341      0.017      1.973      0.049       0.000       0.068\n",
       "x3             0.1215      0.022      5.605      0.000       0.079       0.164\n",
       "                             Regime 2 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.7346      0.136      5.419      0.000       0.469       1.000\n",
       "x1             0.8436      0.024     34.798      0.000       0.796       0.891\n",
       "x2             0.1633      0.032      5.067      0.000       0.100       0.226\n",
       "x3            -0.0499      0.027     -1.829      0.067      -0.103       0.004\n",
       "                           Non-switching parameters                           \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sigma2         0.1660      0.018      9.138      0.000       0.130       0.202\n",
       "                         Regime transition parameters                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "p[0->0]        0.7214      0.117      6.147      0.000       0.491       0.951\n",
       "p[1->0]     4.001e-08      0.035   1.13e-06      1.000      -0.069       0.069\n",
       "p[2->0]        0.0783      0.057      1.372      0.170      -0.034       0.190\n",
       "p[0->1]        0.1044      0.095      1.103      0.270      -0.081       0.290\n",
       "p[1->1]        0.8259      0.054     15.201      0.000       0.719       0.932\n",
       "p[2->1]        0.2288      0.073      3.126      0.002       0.085       0.372\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_fedfunds4.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Due to lower information criteria, we might prefer the 3-state model, with an interpretation of low-, medium-, and high-interest rate regimes. The smoothed probabilities of each regime are plotted below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(3, figsize=(10,7))\n",
    "\n",
    "ax = axes[0]\n",
    "ax.plot(res_fedfunds4.smoothed_marginal_probabilities[0])\n",
    "ax.set(title='Smoothed probability of a low-interest rate regime')\n",
    "\n",
    "ax = axes[1]\n",
    "ax.plot(res_fedfunds4.smoothed_marginal_probabilities[1])\n",
    "ax.set(title='Smoothed probability of a medium-interest rate regime')\n",
    "\n",
    "ax = axes[2]\n",
    "ax.plot(res_fedfunds4.smoothed_marginal_probabilities[2])\n",
    "ax.set(title='Smoothed probability of a high-interest rate regime')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Switching variances\n",
    "\n",
    "We can also accommodate switching variances. In particular, we consider the model\n",
    "\n",
    "$$\n",
    "y_t = \\mu_{S_t} + y_{t-1} \\beta_{S_t} + \\varepsilon_t \\quad \\varepsilon_t \\sim N(0, \\sigma_{S_t}^2)\n",
    "$$\n",
    "\n",
    "We use maximum likelihood to estimate the parameters of this model: $p_{00}, p_{10}, \\mu_0, \\mu_1, \\beta_0, \\beta_1, \\sigma_0^2, \\sigma_1^2$.\n",
    "\n",
    "The application is to absolute returns on stocks, where the data can be found at https://www.stata-press.com/data/r14/snp500."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get the federal funds rate data\n",
    "from statsmodels.tsa.regime_switching.tests.test_markov_regression import areturns\n",
    "dta_areturns = pd.Series(areturns, index=pd.date_range('2004-05-04', '2014-5-03', freq='W'))\n",
    "\n",
    "# Plot the data\n",
    "dta_areturns.plot(title='Absolute returns, S&P500', figsize=(12,3))\n",
    "\n",
    "# Fit the model\n",
    "mod_areturns = sm.tsa.MarkovRegression(\n",
    "    dta_areturns.iloc[1:], k_regimes=2, exog=dta_areturns.iloc[:-1], switching_variance=True)\n",
    "res_areturns = mod_areturns.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>y</td>        <th>  No. Observations:  </th>    <td>520</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovRegression</td> <th>  Log Likelihood     </th> <td>-745.798</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Tue, 24 Dec 2019</td> <th>  AIC                </th> <td>1507.595</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>15:02:26</td>     <th>  BIC                </th> <td>1541.626</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>             <td>05-16-2004</td>    <th>  HQIC               </th> <td>1520.926</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                   <td>- 04-27-2014</td>   <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>approx</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>  <td>    0.7641</td> <td>    0.078</td> <td>    9.761</td> <td> 0.000</td> <td>    0.611</td> <td>    0.918</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>     <td>    0.0791</td> <td>    0.030</td> <td>    2.620</td> <td> 0.009</td> <td>    0.020</td> <td>    0.138</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.3476</td> <td>    0.061</td> <td>    5.694</td> <td> 0.000</td> <td>    0.228</td> <td>    0.467</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>  <td>    1.9728</td> <td>    0.278</td> <td>    7.086</td> <td> 0.000</td> <td>    1.427</td> <td>    2.518</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>     <td>    0.5280</td> <td>    0.086</td> <td>    6.155</td> <td> 0.000</td> <td>    0.360</td> <td>    0.696</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    2.5771</td> <td>    0.405</td> <td>    6.357</td> <td> 0.000</td> <td>    1.783</td> <td>    3.372</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0]</th> <td>    0.7531</td> <td>    0.063</td> <td>   11.871</td> <td> 0.000</td> <td>    0.629</td> <td>    0.877</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0]</th> <td>    0.6825</td> <td>    0.066</td> <td>   10.301</td> <td> 0.000</td> <td>    0.553</td> <td>    0.812</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using numerical (complex-step) differentiation."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                        Markov Switching Model Results                        \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                  520\n",
       "Model:               MarkovRegression   Log Likelihood                -745.798\n",
       "Date:                Tue, 24 Dec 2019   AIC                           1507.595\n",
       "Time:                        15:02:26   BIC                           1541.626\n",
       "Sample:                    05-16-2004   HQIC                          1520.926\n",
       "                         - 04-27-2014                                         \n",
       "Covariance Type:               approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.7641      0.078      9.761      0.000       0.611       0.918\n",
       "x1             0.0791      0.030      2.620      0.009       0.020       0.138\n",
       "sigma2         0.3476      0.061      5.694      0.000       0.228       0.467\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          1.9728      0.278      7.086      0.000       1.427       2.518\n",
       "x1             0.5280      0.086      6.155      0.000       0.360       0.696\n",
       "sigma2         2.5771      0.405      6.357      0.000       1.783       3.372\n",
       "                         Regime transition parameters                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "p[0->0]        0.7531      0.063     11.871      0.000       0.629       0.877\n",
       "p[1->0]        0.6825      0.066     10.301      0.000       0.553       0.812\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical (complex-step) differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_areturns.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first regime is a low-variance regime and the second regime is a high-variance regime. Below we plot the probabilities of being in the low-variance regime. Between 2008 and 2012 there does not appear to be a clear indication of one regime guiding the economy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res_areturns.smoothed_marginal_probabilities[0].plot(\n",
    "    title='Probability of being in a low-variance regime', figsize=(12,3));"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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